4. Consider the following endogenous growth model: a representative household's life-time utility function is given as: ptc(t)10 - 1 e pt dt. 1-0 The production function is: Y(t) = AK(t) Hy(t)l-a where Hp(t) denotes human capital used in production. Human capital accumulation equation is: H(t) = BHE(t) 8H(t), where He(t) is human capital devoted to education. In total we have He(t) + Hp(t) H(t). Denote the fraction of human capital allocated to production by o(t). Please go as far as you can to characterize the balanced growth path of the economy. 4. Consider the following endogenous growth model: a representative household's life-time utility function is given as: ptc(t)10 - 1 e pt dt. 1-0 The production function is: Y(t) = AK(t) Hy(t)l-a where Hp(t) denotes human capital used in production. Human capital accumulation equation is: H(t) = BHE(t) 8H(t), where He(t) is human capital devoted to education. In total we have He(t) + Hp(t) H(t). Denote the fraction of human capital allocated to production by o(t). Please go as far as you can to characterize the balanced growth path of the economy